Merge overlapping vertices of different objects
The start and end caps of an array can themselves be 'live' (unapplied) arrays.



If 'merge' is checked in the array modifier, the start and end caps merge with the arrayed object.

So you can apply the array modifier to your transition object (no repeats) and set your first array as the start cap, and your second array as the end cap of your transition 'array'.